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A spring with a constant of #8 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

Charles Aeschliman

The compression is #=1.5m#

The spring constant is #k=8kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*2*(3)^2=9J#

This kinetic energy will be stored in the spring as potential energy.

#PE=9J#

So,

#1/2kx^2=9#

#x^2=9*2/(8)=2.25m^2#

#x=sqrt(2.25)=1.5m#

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Answer 2

Nicholas Agrusa

The spring will compress by 0.375 meters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.